Transcript Lectures 4-5: The specific factors model Giovanni Facchini

Lectures 4-5: The specific factors model
Giovanni Facchini
Outline
 Introduction
 The specific factors model
 International trade in the specific factors model
 Income distribution and the gains from trade
 The political economy of international trade policy
 Summary
Slide 3-2
Introduction


International trade has important income distribution
consequences within a country.
There are two fundamental reasons for why trade has
important effects on income distribution:
• Production factors cannot instantaneously relocate from
•

one sector to another at zero cost.
Factor’s demand vary by sector.
The specific factors model highlights how trade affects
the income distribution.
Slide 3-3
The specific factors model

Assumptions
• The economy produces two goods, manufactured goods (M)
•
•
•
•
and food (F)
There are three production factors : labor (L), capital (K) and
land (T).
Manufactured goods are produced using capital and labor (but
not land).
Food is produced using land and labor (but not capital).
– Thus labor is mobile because it is used by both sectors
– Land and capital are specific factors that can be used in the
production of one good only.
All markets are perfectly competitive.
Slide 3-4
The specific factors model
• How much of each good is produced?
– The production of manufactured goods depends on the
quantity of labor and capital used in the sector.
• This relationship is captured by the production function.
• The production function for good X characterizes the
maximum quantity of good X that can be produced using
all possible combinations of factors.
– For example, the production function for manufactured
goods (food) tells us the quantity of manufactured goods
(food) that we can produce for any given quantity of capital
(land) and labor.
Slide 3-5
The specific factors model
• The production function for manufactured goods is given
•
by
QM = QM (K, LM)
(3-1)
where:
– QM is the output of manufactured goods
– K is the endowment of capital
– LM is the number of workers employed in the M sector
The production function for manufactured goods is given
by
QF = QF (T, LF)
(3-2)
where:
– QF is the output of food
– T is the endowment of land
– LF is the number of workers employed in the F sector
Slide 3-6
The specific factors model
• The labor market equilibrium under full employment
implies that:
LM + LF = L
(3-3)
• We can use these relationships to construct the
production possibility frontier of the country.
Slide 3-7
The specific factors model
 The production possibility frontier
• To analyze the production possibility frontier of the
country we need to ask how the output mix of the
country varies as labor relocates from one sector to the
other.
• Figure 1 shows the production function for
manufactured goods.
Slide 3-8
The specific factors model
Figure 1: The manufactured goods production function
QM
QM = QM (K, LM)
LM
Slide 3-9
The specific factors model
• The shape of the production function highlights the
presence of decreasing marginal product of labor
– Adding an extra worker to the production process, keeping
capital constant, implies a reduction in the quantity of
capital per worker.
– Therefore, every additional unit of labor will imply an
increase in output at a decreasing rate.
• Figure 2 depicts the marginal productivity of labor, i.e. the
increase of output brought about by an additional unit of
labor.
Slide 3-10
The specific factors model
Figure 2: The marginal product of labor
MPLM
MPLM
LM
Slide 3-11
The specific factors model
Figure 3: The PPF in the specific factors model
QF (increasing )
Food production function
Production possibility frontier(PP)
Q 2F
QF =QF(K, LF)
1'
2'
3'
LF
(increasing)
Q2 M
L2F
L2M
1
2
Labor allocation(AA)
PP
QM (increasing
)
3
AA
LM (increasing )
Manufactured goods
production function
QM =QM(K, LM)
Slide 3-12
Slope of the PP curve
 Ricardian model:
• The PP curve is a straight line because the opportunity
cost of food in terms of manufacturing is constant
 Specific factors model:
• The PP curve illustrates the presence of decreasing
marginal productivity of labor in each sector. The
slope is given by - MPLF /MPLM
• To increase the ooutput of manufactured goods by one
unit, the economy needs to reduce the output of food
by MPLF /MPLM
Slide 3-13
The specific factors model
 Prices, wages and labor allocation
• How much labor will be used by each sector?
– To answer this question, we need to consider the
demand and the supply of labor.
• Labor demand:
– In each sector, employers will try to maximize profits,
hiring workers up to the point in which the marginal
product of labor is equal to the cost of hiring that
additional unit.
Slide 3-14
The firm’s problem
 In each sector, the firm maximizes profits, i.e. it
solves the following problem
max pM QM ( K , LM )  wLM
LM
and the corresponding first order condition is given
by
dQM
pM
w
dLM
Slide 3-15
The specific factors model
• The labor demand curve in the manufacturing sector is
given by
MPLM x PM = w
– The wage is equal to the value of the marginal
product in the manufacturing sector.
• The labor demand in the food sector is instead given
by:
MPLF x PF = w
– Once again, the wage is equal to the value of the
marginal product in the manufacturing sector.
Slide 3-16
The specific factors model
 In equilibrium, the salary has to be the same in the
two sectors, as a result of the perfect mobility of
labor.
 The wage is determined as a result of market
clearing:
LM + LF = L
Slide 3-17
The specific factors model
The allocation of labor between sectors
W
W
1
PF X MPLF
(Labor demand in
the food sector)
W1
PM X MPLM
(Labor demand in the
manufacturing sector)
Labor employed in the
manufacturing
sector,LM
Labor employed in
the food sector , LF
L 1M
L1F
Overall labor supply L
Slide 3-18
Labor demand in the food sector
 In equilibrium, the PPF is tangent to the line whose
slope is given by the relative price of manufacturing
in terms of food (with a minus sign).
 The relationship between relative prices and output
levels is given by :
-MPLF/MPLM = -PM/PF
Slide 3-19
The specific factors model
Figure 5: Output in the specific factors model
QF
Slope = -(PM /PF)1
1
Q1 F
PP
Q1 M
QM
Slide 3-20
The specific factors model
• What happens to the allocation of labor and the
income distribution if the price of food and the price of
the manufactured goods change?
• Two possible scenarios:
– Proportional variation in prices
– Change in relative prices
Slide 3-21
The specific factors model
Proportional increase in the two prices
PM 2 X MPLM
W
PM 1 X MPLM P
M
increases
by 10%
PF increases
by 10%
2
W2
PF 1 X MPLF
Increase by
10% in the
salary
W1
Labor employed in the
manufacturing sector LM
PF 2 X MPLF
W
1
Labor employed in the
Food sector, LF
Slide 3-22
The specific factors model
• When prices change by the same proportion, there is
no effect in real terms.
– The wage (w) increases proportionally with the prices,
and as a result real wages are unaffected.
– The capital- and land- owners real incomes are also
unaffected.
Slide 3-23
The specific factors model
• If only PM increases, labor relocates from the food to
the manufacturing sector and the output level increases
in the manufacturing sector, while it decreases in the
food sector.
• The wage (w) does not increase as much as PM , since
employment in the manufacturing sector increases and
thus the marginal productivity of labor in that sector
decreases.
Slide 3-24
The specific factors model
An increase in the price of manufacturing by 10%
W
Increase in the
relative
demand by
10%
Increase in W 2
the wage
by less than W 1
10%
1
PF X MPLF
W
2
1
PM 2 X MPLM
PM 1 X MPLM
Labor employed in the
manufacturing sector
Quantity of labor
Relocating to
manufacturing
Labor employed in the
Food sector
Slide 3-25
The specific factors model
Figure 8: The effect of a change in the relative price of manufacturing
QF
Solpe= - (PM /PF)1
Q1F
1
Q2F
2
Slope= - (PM /PF) 2
PP
Q1 M
Q2 M
QM
Slide 3-26
The specific factors model
 Relative prices and income distribution
• Assume that PM increases by 10%. Then, we expect an
increase in wages by less than 10%, for example 5%.
• What is the effect of this increase on the income of the
following three groups?
– Workers
– Capital owners
– Landowners
Slide 3-27
The specific factors model
• Workers:
– The effect is indeterminate. It depends on the relative
importance of the consumption of the two goods.
• Capital owners:
– They are better off. The inflow of additional workers in
the manufacturing sector increases the marginal
productivity of capital.
• Land owners:
– They are worse off. The outflow of workers from the
food sector decreases the marginal productivity of land.
Slide 3-28
The specific factors model
Figure 9: Determining relative prices
PM /PF
RS
1
(PM /PF
)1
RD
(QM /QF )1
QM/QF
Slide 3-29
International trade in the specific
factors model
 Assumptions:
• Assume that both countries (say Japan and the US) share
the same preferences and thus the same relative demand.
• Thus the only source of trade is represented by
differences in the relative supply across countries. The
relative supply might differ because of
– technology
– different endowments of production factors (capital, labor,
land)
• We will assume that there are differences in factor
endowments.
Slide 3-30
International trade in the specific factors model
 Endowments and relative supply
• What are the effects of an increase in the capital
endowment on the output of manufactured goods and
food?
– A country with a large endowment of capital will
produce a higher ratio of manufacturing to food for
every given combination of relative prices.
Slide 3-31
International trade in the specific
factors model
Figure 10: An increase in the endowment of capital
W
Increase in
the capital
stock K
PF 1 X MPLF
W
2
W2
1
W1
PM X MPLM2
PM X MPLM1
Labor employed in the
manufacturing sector
Labor relocating to the
manufacturing sector
Labor employed in the
Food sector
Slide 3-32
International trade in the specific factors model
• An increase in the endowment of capital leads to a
shift to the right of the relative supply
• An increase in the endowment of land leads to a shift
to the left of the relative supply
• What happens if the labor supply increases?
– The effect on the relative output level is ambiguous,
even though we know that both outputs will increase.
Slide 3-33
International trade in the specific factors model
 International trade and relative prices
• Assume that Japan (J) has more capital per worker
than the USA (A). Analogously, the USA have more
land per worker than Japan.
– As a result, the relative price of manufactured goods in
autarky is lower in Japan than in the USA.
• International trade brings about a convergence in
relative prices.
Slide 3-34
International trade in the specific
factors model.
Figure 11: International trade and relative prices
PM /PF
RSA
RSWORLD
(PM /PF )A
RSJ
(PM /PF )W
(PM /PF )J
RDWORLD
QM/QF
Slide 3-35
International trade in the specific factors model.
 The structure of trade flows
• In autarky, production must be equal to consumption
• If trade is possible, the combinations of manufactured
goods and food that are consumed might differ from
those that are produced.
• Still, a country cannot spend more than the value of its
output (no borrowing in this model).
Slide 3-36
International trade in the specific factors model.
Figure 12: The budget constraint of a trading economy
Food Consumption, DF
Food Production, QF
Budget constraint
(slope = -PM/PF)
1
Q1 F
PPF
Q1 M
Manufactured consumption, DM
Manufactured production, QM
Slide 3-37
International trade in the specific factors model
Figure 13: Equilibrium under free trade
F
F
Japan’s budget
constraint
US food
exports
J’s food
imports
US budget constraint
QAF
DAF
DJF
QJF
DJM QJM M
J’s manufactured
goods exports
QAM DAM
M
US food imports
Slide 3-38
Income distribution and the gains from
international trade

To assess the effect of trade on income distribution, we
need to remember that international trade changes the
relative good prices .

International trade improves the welfare of the specific
factor used in the sector producing export goods, but it
reduces the welfare of the specific factor used in the
production of import competing goods.

International trade has an ambiguous effect on the
mobile factor.
Slide 3-39
Income distribution and the gains from
international trade

It is possible for those who gains from international trade
to compensate those who lose from it?
• If this is the case, international trade is potentially Pareto
improving, i.e. it can make everybody better off.

International trade increases overall welfare because it
expands the consumption possibility set.
• The expansion of the consumption possibility set implies that
everybody can – potentially at least – be made better off as a
result of international trade.
Slide 3-40
Income distribution and the gains from
international trade
Figure 14: International trade expands the consumption possibilities of
each country
Food consumption, DF
Food production, QF
2
Q1
1
F
Budget constraint
(slope = - PM/PF)
PP
Q1 M
Manuf. consumption, DM
Manuf. production, QM
Slide 3-41
The political economy of trade policy: a
preliminary look


International trade creates winners and losers.
The optimal trade policy
• The government needs to trade off the gains of some
groups against the losses of some other groups
– Some groups ask for protection because they are already
poor (for examples, US workers in the shoe, apparel
industries).
– Most economists are still in favor of open trade policies.
• To understand how trade policies come about, we need
to understand the true reasons behind trade policy
choices.
Slide 3-42
The political economy of trade policy: a
preliminary look
 Income distribution and trade policies
• Usually, those who gain from trade are much less
informed than thos who lose from trade.
– Example: sugar producers and consumers in the United
States.
Slide 3-43
Summary
 International trade has important effects on the
income distribution within a country, thus creating
winners and losers
 Income distribution effects are due to:
• Production factors cannot relocate costlessly between
one sector and the other.
• Changes in the output mix have different effects on
the demand for production factors.
Slide 3-44
Summary
 The specific factors model is a useful tool in the
analysis of the income distribution effects of trade
• In this model, differences in factor endowments might
lead to differences in the relative supply curves and
thus lead to international trade.
• In each country, specific factors used in the exporting
sectors benefit from opening up trade, while the
specific factors used in the import competing sectors
lose.
• The mobile factor, which is used in both sectors, might
gain or lose..
Slide 3-45
Summary
 International trade brings about aggregate gains,
which can be used – at least as a matter of principle –
to compensate the losers, and thus bring about Pareto
gains from trade.
Slide 3-46